Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

D. Sarmany, F. Izsak, Jacobus J.W. van der Vegt

    Research output: Book/ReportReportProfessional

    25 Citations (Scopus)
    49 Downloads (Pure)

    Abstract

    We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages34
    Publication statusPublished - Jan 2010

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1914
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • METIS-270717
    • Numerical mathematics
    • EWI-17325
    • Electromagnetic waves
    • MSC-00A72
    • Scientific computation
    • Finite Element Method
    • IR-69763

    Cite this

    Sarmany, D., Izsak, F., & van der Vegt, J. J. W. (2010). Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. (Memorandum / Department of Applied Mathematics; No. 1914). Enschede: University of Twente, Department of Applied Mathematics.
    Sarmany, D. ; Izsak, F. ; van der Vegt, Jacobus J.W. / Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. Enschede : University of Twente, Department of Applied Mathematics, 2010. 34 p. (Memorandum / Department of Applied Mathematics; 1914).
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    abstract = "We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.",
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    series = "Memorandum / Department of Applied Mathematics",
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    Sarmany, D, Izsak, F & van der Vegt, JJW 2010, Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. Memorandum / Department of Applied Mathematics, no. 1914, University of Twente, Department of Applied Mathematics, Enschede.

    Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. / Sarmany, D.; Izsak, F.; van der Vegt, Jacobus J.W.

    Enschede : University of Twente, Department of Applied Mathematics, 2010. 34 p. (Memorandum / Department of Applied Mathematics; No. 1914).

    Research output: Book/ReportReportProfessional

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    AU - Izsak, F.

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    N2 - We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.

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    KW - IR-69763

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    Sarmany D, Izsak F, van der Vegt JJW. Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations. Enschede: University of Twente, Department of Applied Mathematics, 2010. 34 p. (Memorandum / Department of Applied Mathematics; 1914).